Question: $\dfrac{ 8m + 6n }{ -2 } = \dfrac{ 6m - 9p }{ 3 }$ Solve for $m$.
Multiply both sides by the left denominator. $\dfrac{ 8m + 6n }{ -{2} } = \dfrac{ 6m - 9p }{ 3 }$ $-{2} \cdot \dfrac{ 8m + 6n }{ -{2} } = -{2} \cdot \dfrac{ 6m - 9p }{ 3 }$ $8m + 6n = -{2} \cdot \dfrac { 6m - 9p }{ 3 }$ Multiply both sides by the right denominator. $8m + 6n = -2 \cdot \dfrac{ 6m - 9p }{ {3} }$ ${3} \cdot \left( 8m + 6n \right) = {3} \cdot -2 \cdot \dfrac{ 6m - 9p }{ {3} }$ ${3} \cdot \left( 8m + 6n \right) = -2 \cdot \left( 6m - 9p \right)$ Distribute both sides ${3} \cdot \left( 8m + 6n \right) = -{2} \cdot \left( 6m - 9p \right)$ ${24}m + {18}n = -{12}m + {18}p$ Combine $m$ terms on the left. ${24m} + 18n = -{12m} + 18p$ ${36m} + 18n = 18p$ Move the $n$ term to the right. $36m + {18n} = 18p$ $36m = 18p - {18n}$ Isolate $m$ by dividing both sides by its coefficient. ${36}m = 18p - 18n$ $m = \dfrac{ 18p - 18n }{ {36} }$ All of these terms are divisible by $18$ $m = \dfrac{ {1}p - {1}n }{ {2} }$